ELEMENTARY ALGEBRA

ALGEBRAIC EXPRESSION :-  Numbers and literals connected with the operations $+\, ,-\, ,\times \, and\, \div $ form algebraic expression.
       For eg. :-  $3x\, +\, 5y$
       The several parts of an expression connected by the signs + and - are called TERMS of the expression.
       Every term of algebraic expression consists of a variable and constant.

CONSTANT :-  A number or literal having fixed numerical value is called a constant.

VARIABLE :-  A literal whose value varies from one situation to another is called a variable.


TYPES OF ALGEBRAIC EXPRESSION :-

1.   MONOMIAL :-  An algebraic expression consisting of one term is called a monomial.

      For eg. :-  $3x\, ,\, 4x^{2}$ etc.

2.   BINOMIAL :-  An algebraic expression consisting of two terms is called a binomial.

      For eg, :-  $3x\, +\, 7y\, ,\, 3p^{2}\, +\, 2q$ etc.

3.   TRINOMIAL :-  An algebraic expression consisting of three terms is called a trinomial.

       For eg. :-  $3x\, +\, 5y\,+\,  7$

4.   POLYNOMIAL :-  An algebraic expression consisting of one or more terms is polynomial.

       For eg. :-  $3x^{2}\, +\, 2x^{2}\,-\, 4x\, +\, 7$

COEFFICIENT AND DEGREE OF AN ALGEBRAIC EXPRESSION :-

• In any term of an algebraic expression, any of the factors along with the sign of the term, is called the coefficient of the product of the other factors.
• The highest exponent of a polynomial in one variable and the highest power of the sum of the exponents of a polynomial in more than one variable is called degree of the polynomial.

       For eg. :-  $\frac{2}{3}xy^{2}\,+\,7xy^{3}\,-\,\frac{5}{2}x^{3}y^{2}$
         
            Here    $\frac{2}{3}$ is the coefficient of $xy^{2}$

                        7 is the coefficient of $xy^{3}$

                      $-\frac{5}{2}$ is the coefficient $x^{3}y^{2}$

       and,  degree of $\frac{2}{3}xy^{2}$ = 1 + 2 = 3

                degree of $7xy^{3}$ = 1 + 3 = 4

                degree of $-\frac{5}{2}x^{3}y^{2}$ = 3 + 2 = 5

         $\therefore$   Degree of above polynomial is 5.

LIKE AND UNLIKE TERMS :- 

• Terms having same variables with same exponents are called like terms.

          For eg. :-  $6x^{2}\, +\, 2x^{2}$.

• Terms having different variable with different exponents are called unlike terms.

           For eg. :-  $9xy^{2}\, -\, 5x^{2}y$.